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arXiv · 1711.09526

An infinite quantum Ramsey theorem

Matthew Kennedy·Taras Kolomatski·Daniel Spivak
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Abstract

We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided there is no obvious obstruction, there is an infinite rank projection P with the property that the compression PVP is either maximal or minimal in a certain natural sense.

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Matthew Kennedy, Taras Kolomatski, Daniel Spivak. 2017-11-27. An infinite quantum Ramsey theorem. https://arxiv.org/abs/1711.09526

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